Exhibit 10.1

ANSYS, INC.

LONG-TERM INCENTIVE PLAN

1. Purpose

This Long-Term Incentive Plan (the “Plan”) is intended to provide an incentive for superior work and to motivate executives and employees of ANSYS, Inc. (the “Company”) toward even higher achievement and business results, to tie their goals and interests to those of the Company and its stockholders and to enable the Company to attract and retain highly qualified executives and employees. The Plan is for the benefit of Participants (as defined below). Awards made under this Plan constitute Deferred Stock Awards under Section 9 of the Company’s Third Amended and Restated 1996 Stock Option and Grant Plan (the “1996 Option Plan”) and shall be granted under, and subject to, the terms of the 1996 Option Plan.

2. Definitions

For purposes of this Plan:

(a) “Award” means a grant to a Participant hereunder. From and after a Change in Control, any references to an Award shall mean the fixed number of Restricted Stock Units eligible to be earned by a Participant, as determined by the Committee pursuant to Section 6 hereof.

(b) “Award Notice” means a notice or agreement provided to a Participant that sets forth the terms, conditions and limitations of the Participant’s participation in this Plan, including, without limitation, the Participant’s Target Award.

(c) “Board” means the Board of Directors of the Company.

(d) “Cause” means, and shall be limited to a determination by the Company that the Participant’s employment shall be terminated as a result of any one or more of the following events:

(i) any material breach by the Participant of any agreement between the Participant and the Company; or

(ii) the conviction of, indictment for or plea of nolo contendere by the Participant to a felony or a crime involving moral turpitude; or

(iii) any material misconduct or willful and deliberate non-performance (other than by reason of disability) by the Participant of the Participant’s duties to the Company; or

(iv) willful failure to cooperate with a bona fide internal investigation or an investigation by regulatory or law enforcement authorities, after being instructed by the Company to cooperate, or the willful destruction or failure to preserve documents or other materials known to be relevant to such investigation or the willful inducement of others to fail to cooperate or to produce documents or other materials in connection with such investigation.

(e) “Change in Control” means any of the following:

(i) any “person,” as such term is used in Sections 13(d) and 14(d) of the Securities Exchange Act of 1934, as amended (the “Act”) (other than the Company, any of its subsidiaries, or any trustee, fiduciary or other person or entity holding securities under any employee benefit plan or trust of the Company or any of its subsidiaries), together with all “affiliates” and “associates” (as such terms are defined in Rule 12b-2 under the Act) of such person, shall become the “beneficial owner” (as such term is defined in Rule 13d-3 under the Act), directly or indirectly, of securities of the Company representing 50 percent or more of the combined voting power of the Company’s then outstanding securities having the right to vote in an election of the Board (“Voting Securities”) (in such case other than as a result of an acquisition of securities directly from the Company); or

(ii) the consummation of (A) any consolidation or merger of the Company where the stockholders of the Company, immediately prior to the consolidation or merger, would not, immediately after the consolidation or merger, beneficially own (as such term is defined in Rule 13d-3 under the Act), directly or indirectly, shares representing in the aggregate more than 50 percent of the voting shares of the Company issuing cash or securities in the consolidation or merger (or of its ultimate parent corporation, if any), or (B) any sale or other transfer (in one transaction or a series of transactions contemplated or arranged by any party as a single plan) of all or substantially all of the assets of the Company.

Notwithstanding the foregoing, a “Change in Control” shall not be deemed to have occurred for purposes of the foregoing clause (i) solely as the result of an acquisition of securities by the Company which, by reducing the number of shares of Voting Securities outstanding, increases the proportionate number of Voting Securities beneficially owned by any person to 50 percent or more of the combined voting power of all of the then outstanding Voting Securities; provided, however, that if any person referred to in this sentence shall thereafter become the beneficial owner of any additional shares of Voting Securities (other than pursuant to a stock split, stock dividend, or similar transaction or as a result of an acquisition of securities directly from the Company) and immediately thereafter beneficially owns 50 percent or more of the combined voting power of all of the then outstanding Voting Securities, then a “Change in Control” shall be deemed to have occurred for purposes of the foregoing clause (i).

(f) “Change in Control Date” means with respect to each Change in Control Performance Measurement Period, the last day of the month immediately preceding the effective date of the Change in Control.

(g) “Change in Control Performance Measurement Period” means the Performance Measurement Period that is shortened by the Committee such that each such period shall be deemed to have concluded as of as of the Change in Control Date.

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(h) “Change in Control Terminating Event” means during the 18-month period following the occurrence of a Change in Control, any of the following events: (i) termination by the Company of the Participant’s employment for any reason other than for Cause, death or disability; or (ii) the termination by the Participant of his or her employment with the Company for Good Reason. Notwithstanding the foregoing, a Change in Control Terminating Event shall not be deemed to have occurred herein solely as a result of the Participant being an employee of any direct or indirect successor to the business or assets of the Company.

(i) “Closing Index Value” means the Performance Measurement Index Value as of the last day of any Performance Measurement Period.

(j) “Closing Stock Price” means the Stock Price as of the last day of any Performance Measurement Period.

(k) “Code” means Internal Revenue Code of 1986, as amended.

(l) “Committee” means the Compensation Committee of the Board.

(m) “Effective Date” means February 17, 2010, the date this Plan was approved by the Committee.

(n) “Good Reason” means that the Participant has complied with the “Good Reason Process” (hereinafter defined) following the occurrence of any of the following events:

(i) a material diminution in the Participant’s responsibilities, authority or duties; or

(ii) a material reduction in the Participant’s Base Salary and Target Bonus except for across-the-board salary reductions similarly affecting all or substantially all management employees; or

(iii) a material change in the geographic location at which the Participant is principally employed.

For purposes of this Section 2(n)(i), a change in the reporting relationship, or a change in a title will not, by itself, be sufficient to constitute a material diminution of responsibilities, authority or duty.

(o) “Good Reason Process” means:

(i) the Participant reasonably determines in good faith that a “Good Reason” condition has occurred;

(ii) the Participant notifies the Company in writing of the occurrence of the Good Reason condition within 60 days of the first occurrence of such condition;

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(iii) the Participant cooperates in good faith with the Company’s efforts, for a period not less than 30 days following such notice (the “Cure Period”), to remedy the condition;

(iv) notwithstanding such efforts, the Good Reason condition continues to exist following the Cure Period; and

(v) the Participant terminates his or her employment within 30 days after the end of the Cure Period.

If the Company cures the Good Reason condition during the Cure Period, Good Reason shall be deemed not to have occurred.

(p) “Initial Index Value” means, the Performance Measurement Index Value as of the first day of any Performance Measurement Period.

(q) “Initial Stock Price” means the Stock Price as of the first day of any Performance Measurement Period.

(r) “Participant” means an executive or employee of the Company selected by the Committee to participate in the Plan.

(s) “Performance Measurement Index” means the NASDAQ Composite Total Returns Index, or, in the event such index is discontinued or its methodology significantly changed, a comparable index selected by the Committee in good faith.

(t) “Performance Measurement Index Value” means, with respect to any date, the average value of the Performance Measurement Index for the ten consecutive trading days immediately preceding such date.

(u) “Performance Measurement Period” means, a three calendar year period commencing on January 1, 2010 and each January 1 thereafter while this Plan is effective, and concluding on December 31 of the second calendar year thereafter. There shall be overlapping Performance Measurement Periods.

(v) “Restricted Stock Units” means the restricted stock units of the Company.

(w) “Stock” means the Company’s common stock, par value $0.01 per share.

(x) “Stock Price” means, as of a particular date, the average closing price of one share of Stock for the ten consecutive trading days ending on, and including, such date; provided however, that in the event of a Change in Control of the Company, the Stock Price shall equal the fair market value, as determined by the Committee in its discretion, of the total consideration paid or payable in the transaction resulting in the Change in Control for one share of Stock.

(y) “Target Award” means the target number of Restricted Stock Units that comprise a Participant’s Award for each Performance Measurement Period, as set forth in the Participant’s Award Notice.

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(z) “Total Shareholder Return” means, with respect to a Performance Measurement Period, the total percentage return per share, achieved by the Stock assuming contemporaneous reinvestment in the Stock of all dividends and other distributions (excluding dividends and distributions paid in the form of additional shares of Stock) at the closing price of one share of Stock on the date such dividend or other distribution was paid, based on the Initial Stock Price and the Closing Stock Price for such Performance Measurement Period.

3. Administration

(a) The Plan shall be administered by the Committee. The Committee shall have the discretionary authority to make all determinations (including, without limitation, the interpretation and construction of the Plan and the determination of relevant facts) regarding the entitlement to any Award hereunder and the amount of any Award to be paid under the Plan (including the number of shares of Stock issuable to any Participant), provided such determinations are made in good faith and are consistent with the purpose and intent of the Plan. In particular, but without limitation and subject to the foregoing, the Committee shall have the authority:

(i) to select Participants under the Plan;

(ii) to determine the Target Award and any formula or criteria for the determination of the Target Award for each Participant;

(iii) to determine the terms and conditions, not inconsistent with the terms of this Plan, which shall govern Award Notices and all other written instruments evidencing an Award hereunder, including the waiver or modification of any such conditions;

(iv) to adopt, alter and repeal such administrative rules, guidelines and practices governing the Plan as it shall from time to time deem advisable; and

(v) to interpret the terms and provisions of the Plan and any Award granted under the Plan (and any Award Notices or other agreements relating thereto) and to otherwise supervise the administration of the Plan.

(b) Notwithstanding anything herein to the contrary, the Committee may, in its discretion, make appropriate adjustments to any Award, any Target Award, any Initial Stock Price, any Closing Stock Price or the Total Shareholder Return for any period in connection with or as a result of any of the following events which occur or have occurred after the Effective Date: reorganization, recapitalization, reclassification, stock dividend, stock split, reverse stock split or other similar change in the Company’s capital stock, if the outstanding shares of Stock are increased or decreased or are exchanged for a different number or kind of shares or other securities of the Company, or additional shares or new or different shares or other securities of the Company or other non-cash assets are distributed with respect to such shares of Stock or other securities.

(c) Subject to the terms hereof, all decisions made by the Committee pursuant to the Plan shall be final, conclusive and binding on all persons, including the Company and the Participants. No member of the Board or the Committee, nor any officer or employee of the

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Company acting on behalf of the Board or the Committee shall be personally liable for any action, determination or interpretation taken or made in good faith with respect to the Plan, and all members of the Board or Committee and each and any officer or employee of the Company acting on their behalf shall, to the extent permitted by law, be fully indemnified and protected by the Company in respect of any such action, determination or interpretation.

4. Determination and Payment of Awards

(a) Each Participant’s Award Notice shall specify such Participant’s Target Award for each Performance Measurement Period. The Target Award shall be expressed as a number of Restricted Stock Units.

(b) The Target Award for any Performance Measurement Period shall vest based on the Company’s performance for such Performance Measurement Period as measured by the Total Shareholder Return relative to the median percentage appreciation of the Performance Measurement Index for such Performance Measurement Period as set forth below, subject to the Participant’s continued employment with the Company through the conclusion of the Performance Measurement Period, except as set forth in Section 6 below. The percentage appreciation of the Performance Measurement Index shall be established by comparing the Initial Index Value to the Closing Index Value.

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For purposes of clarity, if the Total Shareholder Return for a Performance Measurement Period does not equal or exceed 91% of the median percentage appreciation of the Performance Measurement Index for the Performance Measurement Period, no portion of the Target Award shall vest.

(c) The Committee, at its first meeting following the conclusion of each Performance Measurement Period, shall determine the actual number of Restricted Stock Units that will be deemed to have vested as of the final day of the Performance Measurement Period, in accordance with Schedule A, attached hereto.

(d) As soon as practicable (but in no event later than 74 days) following the conclusion of the applicable Performance Measurement Period, the vested Restricted Stock Units, if any, will be settled in an equal number of shares of Stock.

5. Termination of Employment. Unless otherwise provided in any Award Notice or as provided in Section 6 below, if at any time prior to the conclusion of any Performance Measurement Period, a Participant’s employment with the Company terminates for any reason, such Participant shall automatically forfeit the right to receive any Award not vested as of the date of termination of employment.

6. Change in Control. Unless otherwise provided in any Award Notice, upon a Change in Control of the Company, the following shall occur:

(a) With respect to each Change In Control Performance Measurement Period, the Committee, in accordance with Section 4, shall determine the actual number of Restricted Stock Units that are eligible to be earned based on the Total Shareholder Return for the Change in Control Performance Measurement Period relative to the median percentage appreciation of the Performance Measurement Index for such Change in Control Performance Measurement Period and such Award shall not be deemed fully vested until the conclusion of the original Performance Measurement Period, subject to the continued employment of the Participant through such date. For example, if a Change in Control occurs during the 12 ^th month of a Performance Measurement Period, after the Committee has determined the number of Restricted Stock Units that are eligible to be earned with respect to the applicable Change in Control Performance Measurement Period based on performance for such period, the Award shall not be deemed fully vested until the end of the 36^th month of the original Performance Measurement Period. For the avoidance of doubt, since the Plan contemplates overlapping Performance Measurement Periods, there may be up to two different Change In Control Performance Measurement Periods.

(b) In the event that subsequent to a Change in Control, a Participant’s employment with the Company terminates for any reason other than a Change in Control Terminating Event, such Participant shall automatically forfeit the right to receive all outstanding Awards not vested as of the date of termination of employment.

(c) In the event a Change in Control Terminating Event occurs with respect to a Participant, all outstanding Awards held by such Participant shall immediately vest and become payable.

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(d) If as a result of a Change in Control, no Stock remains outstanding and the surviving corporation (or its ultimate parent) does not agree to convert the Awards into a number of restricted stock units of equivalent value of the surviving corporation (or its ultimate parent), then the Awards shall be converted to a dollar value based on the Stock Price.

7. Miscellaneous

(a) Amendment and Termination. The Company reserves the right to amend or terminate the Plan at any time in its discretion without the consent of any Participants, but no such amendment shall adversely affect the rights of the Participants with regard to outstanding Awards. In the event the Plan is terminated, the Company shall determine the Awards payable to Participants based on the Total Shareholder Return relative to the Performance Measurement Index for each Performance Measurement Period ending on the date of Plan termination. The Awards for each Performance Measurement Period shall be further prorated to reflect the shortened Performance Measurement Period.

(b) No Contract for Continuing Services. This Plan shall not be construed as creating any contract for continued services between the Company or any of its subsidiaries and any Participant and nothing herein contained shall give any Participant the right to be retained as an employee or consultant of the Company or any of its subsidiaries.

(c) No Transfers. A Participant’s rights in an interest under the Plan may not be assigned or transferred.

(d) Unfunded Plan. The Plan shall be unfunded and shall not create (or be construed to create) a trust or separate fund. Likewise, the Plan shall not establish any fiduciary relationship between the Company or any of subsidiaries or affiliates and any Participant. To the extent that any Participant holds any rights by virtue of an Award under the Plan, such right shall be no greater than the right of an unsecured general creditor of the Company or any of its subsidiaries.

(e) Governing Law. The Plan and each Award Letter awarded under the Plan shall be construed in accordance with and governed the laws of the State of Delaware, without regard to principles of conflict of laws of such state.

(f) Tax Withholding. Any issuance of shares of Stock to a Participant shall be subject to tax withholding. The minimum tax withholding obligation shall be satisfied through a net issuance of shares. The Company shall withhold from shares of Stock to be issued to the Participant a number of shares of Stock with an aggregate fair market value that would satisfy the minimum withholding amount due.

(g) Construction. Wherever appropriate, the use of the masculine gender shall be extended to include the feminine and/or neuter or vice versa; and the singular form of words shall be extended to include the plural; and the plural shall be restricted to mean the singular.

(h) Headings. The Section headings and Section numbers are included solely for ease of reference. If there is any conflict between such headings or numbers and the text of this Plan, the text shall control.

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(i) Effect on Other Plans. Nothing in this Plan shall be construed to limit the rights of Participants under the Company’s or its subsidiaries’ benefit plans, programs or policies.

(j) Effective Date. The Plan shall be effective as of the Effective Date.

8. Section 409A.

(a) All payments and benefits described in this Plan are intended to constitute a short term deferral for purposes of Section 409A of the Internal Revenue Code of 1986, as amended. To the extent that any payment or benefit described in this Plan constitutes “non-qualified deferred compensation” under Section 409A of the Code, and to the extent that such payment or benefit is payable upon the Covered Executive’s termination of employment, then such payments or benefits shall be payable only upon the Covered Executive’s “separation from service.” The determination of whether and when a separation from service has occurred shall be made in accordance with the presumptions set forth in Treasury Regulation Section 1.409A-1(h).

(b) The parties intend that this Plan will be administered in accordance with Section 409A of the Code. To the extent that any provision of this Plan is ambiguous as to its compliance with Section 409A of the Code, the provision shall be read in such a manner so that all payments hereunder comply with Section 409A of the Code. The parties agree that this Plan may be amended, as reasonably requested by either party, and as may be necessary to fully comply with Section 409A of the Code and all related rules and regulations in order to preserve the payments and benefits provided hereunder without additional cost to either party.

(c) The Company makes no representation or warranty and shall have no liability to the Covered Executive or any other person if any provisions of this Plan are determined to constitute deferred compensation subject to Section 409A of the Code but do not satisfy an exemption from, or the conditions of, such Section.

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